The compelling synthesis results of Generative Adversarial Networks (GANs) demonstrate rich semantic knowledge in their latent codes. To obtain this knowledge for downstream applications, encoding GANs has been proposed to learn encoders, such that real world data can be encoded to latent codes, which can be fed to generators to reconstruct those data. However, despite the theoretical guarantees of precise reconstruction in previous works, current algorithms generally reconstruct inputs with non-negligible deviations from inputs. In this paper we study this predicament of encoding GANs, which is indispensable research for the GAN community. We prove three uncertainty principles of encoding GANs in practice: a) the perfect' encoder and generator cannot be continuous at the same time, which implies that current framework of encoding GANs is ill-posed and needs rethinking; b) neural networks cannot approximate the underlying encoder and generator precisely at the same time, which explains why we cannot getperfect' encoders and generators as promised in previous theories; c) neural networks cannot be stable and accurate at the same time, which demonstrates the difficulty of training and trade-off between fidelity and disentanglement encountered in previous works. Our work may eliminate gaps between previous theories and empirical results, promote the understanding of GANs, and guide network designs for follow-up works.